Right now, if you have a 3-maniplex and you want to see how the faces etc fit together by sketching it on paper, Ramp does not really facilitate that interaction. For example, when I wanted to understand the structure of a map whose 2-holes were self-intersecting, I had to basically work with one flag at a time and carefully follow its orbit under one subgroup and then another...
If we were able to label the vertices, then we could say things like "this hole visits vertices in the order 1 3 2 4" rather than looking at the sequence of flags.
I guess a straightforward way to do this would be by labeling vertices (faces, other sections, ...) in order by the minimal flag they contain. For example, for vertices, we look at the orbits of <r1, ..., r_{n-1}>, and then v_1 is the orbit of 1, v_2 is the orbit of the smallest flag not in v_1, etc.
Finally, being able to label vertices makes it possible to do things like truncate a single vertex (see #73 )
CunningGabe
commented
1 year ago
Right now, if you have a 3-maniplex and you want to see how the faces etc fit together by sketching it on paper, Ramp does not really facilitate that interaction. For example, when I wanted to understand the structure of a map whose 2-holes were self-intersecting, I had to basically work with one flag at a time and carefully follow its orbit under one subgroup and then another...
If we were able to label the vertices, then we could say things like "this hole visits vertices in the order 1 3 2 4" rather than looking at the sequence of flags.
I guess a straightforward way to do this would be by labeling vertices (faces, other sections, ...) in order by the minimal flag they contain. For example, for vertices, we look at the orbits of <r1, ..., r_{n-1}>, and then v_1 is the orbit of 1, v_2 is the orbit of the smallest flag not in v_1, etc.
Finally, being able to label vertices makes it possible to do things like truncate a single vertex (see #73 )